Eurobank is the 17th largest Polish bank with assets of 14 billion zloty ($3.9 billion), and is more than 20 times smaller than the country’s biggest lender PKO BP (PKO.WA). Last year, it made a net profit of 103 million zloty.

“Eurobank is in a sale process. SocGen is withdrawing (from retail banking activities) in Poland,” one of the bankers said, while another banker confirmed that Eurobank is for sale. Neither wished to be identified as talks are private.

“(SocGen’s) strategy is to gain 1st to 3rd place in every market. Since it hasn’t happened here, they are to withdraw,” the first source said. “The question is who will buy Eurobank, as buyers such as BNP and Santander recently bought smaller banks.”

The sale of Eurobank would underpin a broader trend of consolidation in Poland’s banking sector, which has accelerated in recent years with the ruling eurosceptic Law and Justice (PiS) party encouraging domestic ownership.

Societe Generale has said that it would dispose or close sub-scale entities that bring low synergies.

“Societe Generale doesn’t comment on market rumors,” a spokesman for France’s third-largest bank said about a potential sale of Eurobank.

SocGen has strong market shares in the Czech Republic and Romania, where it has also based its back office.

The bank has a 1.1 percent market share in Poland when taking into account its stock of customer loans, according to a presentation to investors. Its French rival BNP Paribas (BNPP.PA), which recently agreed to acquire Raiffeisen Bank International’s (RBI) (RBIV.VI) main business in Poland, has a 6 percent market share in loans and deposits.

The Polish government has also entered the fray, with state entities buying a near 33 percent stake in Bank Pekao SA (PEO.WA), Poland’s second largest lender, from Italy’s UniCredit (CRDI.MI) last year.

The 10.6 billion zloty deal allowed the government to claim that Polish ownership of the sector rose to 55 percent, outpacing foreign investors who dominated Polish banks for years.

It was not immediately clear who would be interested in buying Eurobank, with natural candidates such as Spain’s Santander (SAN.MC) and BNP already busy with other deals. Some bankers speculate that state-run PKO BP may be interested, while others suggest Credit Agricole (CAGR.PA) - another French giant that lacks scale in Poland.

Credit Agricole said in February that it wanted to expand in Poland.

“Our priority is organic growth in Poland, but ... when there are opportunities we are able to take opportunities,” Credit Agricole’s Chief Executive Officer Philippe Brassac has said.

PKO has also said that it wants to grow organically but would be open to other opportunities that arise.

Poland is a fast-growing economy, but some investors are worried that the state, which has taken over assets in the energy sector as well as banking, exerts too much power over business.

Additional reporting by Maya Nikolaeva and Matthieu Protard in Paris and Agnieszka Barteczko in Warsaw; Editing by Susan Fenton